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Nonconforming FEMs for the $p$-Laplace Problem

Nonconforming FEMs for the $p$-Laplace Problem
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Year:    2018

Author:    D. J. Liu, A. Q. Li, Z. R. Chen

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1365–1383

Abstract

The $p$-Laplace problems in topology optimization eventually lead to a degenerate convex minimization problem $E(v):= ∫_ΩW(∇v)dx − ∫_Ωf vdx$ for $v∈W^{1,p}_0(Ω)$ with unique minimizer $u$ and stress $σ := DW(∇u)$. This paper proposes the discrete Raviart-Thomas mixed finite element method (dRT-MFEM) and establishes its equivalence with the Crouzeix-Raviart nonconforming finite element method (CR-NCFEM). The sharper quasi-norm a priori and a posteriori error estimates of this two methods are presented. Numerical experiments are provided to verify the analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0117

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1365–1383

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Adaptive finite element methods nonconforming $p$-Laplace problem dual energy.

Author Details

D. J. Liu

A. Q. Li

Z. R. Chen

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